Cardinality ≤2c\leq 2^{\mathfrak c} or Smaller or same as the power set of the continuum ,Cardinality ≤ℶ1\leq\beth_1

There exists an injective function from the space into P(R)P(\mathbb{R}), the set of subsets of R\mathbb{R}.

See sections 1.12-1.15 of MR MR2048350.

Id Spaces Value Source
1 Discrete topology on a two-point set
19 Compact Complement Topology for the Euclidean Real Numbers
39 Closed long ray
40 Altered long ray
41 Lexicographic unit square
42 Right Ray Topology on the Reals
44 Nested interval topology
45 Overlapping interval topology
54 Double pointed reals
85 Line with uncountably many origins
99 Alexandroff square
103 Continuum-power of closed unit intervals
104 Product of the first-uncountable ordinal with the continuum-power of unit intervals
107 Countable box product of reals
108 Stone-Cech compactification of the integers
110 Strong ultrafilter topology
128 Miller's biconnected set
134 Radial metric on the plane
135 Radial intervals through the origin of the plane
136 Bing's discrete extension space
137 Michael's closed subspace